00000cmm a22000004a 4500 UP-99796217611212269 Buklod 20230215085534.0 m go j cr |nu|||auu|a 111024s2011 xx u | eng d 9783642236501 (eBook) (iLib)UPD-00215704023 DLC DML eng DMLUC QA 614.835 M39 2011eb Mayer, Volker Distance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry [electronic resource] by Volker Mayer, Mariusz Urbanski, Bartlomiej Skorulski. 1st ed. Heidelberg New York Springer-Verlag Berlin Heidelberg c2011 1 online resource (x, 112 p.) ill. (some col.) Lecture Notes in Mathematics 1 Introduction -- 2 Expanding Random Maps -- 3 The RPF theorem -- 4 Measurability, Pressure and Gibbs Condition -- 5 Fractal Structure of Conformal Expanding Random Repellers -- 6 Multifractal Analysis -- 7 Expanding in the Mean -- 8 Classical Expanding Random Systems -- 9 Real Analyticity of Pressure. IP-based subscription, access limited to within on campus computer network. Access via Electronic Resources of the UPD University Library Website. The theory of random dynamical systems originated from stochastic differential equations. It is intended to provide a framework and techniques to describe and analyze the evolution of dynamical systems when the input and output data are known approximately, according to some probability distribution. The development of this field, in both the theory and applications, has gone in many directions. In this manuscript we introduce measurable expanding random dynamical systems, develop the thermodynamical formalism and establish, in particular, the exponential decay of correlations and analyticity of the expected pressure although the spectral gap property does not hold. This theory is then used to investigate fractal properties of conformal random systems. We prove a Bowen's formula and develop the multifractal formalism of the Gibbs states. Depending on the behavior of the Birkhoff sums of the pressure function we arrive at a natural classification of the systems into two classes: quasi-deterministic systems, which share many properties of deterministic ones; and essentially random systems, which are rather generic and never bi-Lipschitz equivalent to deterministic systems. We show that in the essentially random case the Hausdorff measure vanishes, which refutes a conjecture by Bogenschutz and Ochs. Lastly, we present applications of our results to various specific conformal random systems and positively answer a question posed by Bruck and Buger concerning the Hausdorff dimension of quadratic random Julia sets. Electronic reproduction. New York SpringerLink 2011. Available via World Wide Web through SpringerLink. Random dynamical systems. Fractals. Urbanski, Mariusz. Skorulski, Bartlomiej. SpringerLink (Online service). Electronic Resource Available for University of the Philippines Diliman via SpringerLink. Click here to access https://link.springer.com/book/10.1007/978-3-642-23650-1 FO Monograph UPD DMLR Electronic Resource